An impact equivalent test method based on energy accumulation

Abstract

This invention discloses an impact equivalent test method based on energy accumulation, relating to the field of dynamic impact testing under inertial loads. The method first establishes a physical analysis model under overload impact and determines the form of the external inertial load; using this physical model, it establishes the governing equations, geometric equations, and constitutive equations of the structure; it calculates the elastoplastic response process using discrete difference techniques and obtains the corresponding energy values; it compares and selects the principal energy and plots an energy accumulation contour map; it extracts the energy accumulation contour lines and performs numerical fitting to determine a suitable fitting function; and it establishes an equivalent relationship between long and short pulse widths based on the selected fitting function. This invention fully considers the dynamic response process of the structure under elastoplastic theory, establishes an equivalent criterion between long and short pulse widths from the perspective of energy accumulation, provides guidance for the selection of inertial load parameters required for dynamic impact environments, and further promotes the engineering process of equivalent methods for extreme overload simulation environment tests.

Description

Technical Field

[0001] This invention relates to the field of dynamic impact testing under inertial loads, specifically to an impact equivalent test method based on energy accumulation, which is suitable for simulating dynamic impact environments under two different inertial loads and achieving accurate simulation of extreme overload environments. Background Technology

[0002] The pulse duration of overload impacts can range from tens of microseconds to tens of milliseconds. The factors causing system failure due to impact are not only related to the impact overload amplitude but also closely related to the acceleration pulse width. Real-time testing of systems under long-pulse-width impacts is the most direct and effective method for evaluating their performance. However, real-time testing is complex and expensive. Conventional low-cost simulation methods can simulate impact overload environments to some extent, but the pulse width of the resulting impact overload pulses typically does not exceed 100 μs.

[0003] Due to the mismatch in impact pulse widths, significant differences exist in test results across various overload conditions. Therefore, it is necessary to establish equivalent models and methods for long / short pulse width impact loads. However, currently proposed strain equivalence principles rely heavily on experimental and simulation data, making them overly empirical and difficult to generalize. Therefore, there is an urgent need to develop a widely applicable impact equivalence method based on impact dynamics theory for selecting the inertial load parameters required in dynamic impact environments, thereby achieving accurate simulation of extreme overload environments. Summary of the Invention

[0004] To address the problem of acceleration pulse width mismatch and difficulty in achieving equivalent evaluation among different existing impact testing methods, this invention provides an impact equivalent testing method based on energy accumulation.

[0005] This invention, combining elastoplastic theory, analyzes the elastoplastic dynamic response process of the sensitive structure of a sensor under inertial overload impact. From the perspective of energy accumulation, it establishes an equivalent relationship between the peak overload acceleration and pulse width, providing guidance for selecting the inertial load parameters required for dynamic impact environments. Furthermore, it provides theoretical and experimental basis for the impact equivalent evaluation of high overload sensors under high overload at different pulse widths. This invention is achieved through the following technical solution:

[0006] An impact equivalent test method based on energy accumulation includes the following steps:

[0007] (1) Establish a theoretical analysis model under inertial impact. The model is a simplified physical model of the sensitive structure of the sensor device, which can meet the dynamic overload response analysis.

[0008] (2) Based on the measured acceleration data from the overload impact test, determine the external inertial load of the simplified physical model in step (1). The form;

[0009] (3) Under the inertial load determined in step (2), perform force analysis on the micro-segment elements contained in the physical model;

[0010] (4) Based on the force analysis in step (3), establish the governing equations and geometric equations of the physical model;

[0011] (5) Based on the actual inertial device, select the material parameters of the physical model and determine the constitutive relation of the ideal elastoplastic material, as shown in the following equation:

[0012] (1)

[0013] In the formula, E is the Young's modulus of the material. The instantaneous stress of the material during loading. The instantaneous strain of the material during loading. The elastic limit strength of the material. The strain corresponding to the elastic limit strength of the material;

[0014] (6) Based on the constitutive relation of step (5), calculate the mechanical parameters of the physical model, as shown in the following equation:

[0015] (2)

[0016] In the formula, M is the instantaneous bending moment of the structure, N is the instantaneous axial force of the structure, z is the distance from any point on the structure to the neutral axis of the interface, and A represents the cross-sectional area of ​​the structure.

[0017] (7) Determine the initial and boundary conditions of the elastoplastic response process based on the physical model;

[0018] (8) Using the finite difference technique, the governing equations, geometric equations, constitutive relations and mechanical parameters in steps (4) to (6) are discretized into finite difference forms. Under the initial conditions and boundary conditions in step (7), the structure is calculated under inertial loads. The time history response process of all nodes;

[0019] (9) Based on the dynamic response results obtained in step (8), calculate the work done by the external forces on the structure using the following formula. ,kinetic energy and elastic deformation energy :

[0020] (3)

[0021] In the formula, For the j-th discrete time, The time step of the discrete difference is... Let be the deflection at the nth node at time j. , Let represent the instantaneous velocities of the i-th node at time j in the x and y directions, respectively. , Let these represent the instantaneous bending moment and axial force at the i-th node at time j, respectively. Let the inertial force at time j be denoted as . , Let these represent the mass and length of the i-th micro-segment unit, respectively. Represents the second moment of the structure;

[0022] (10) According to the law of conservation of energy, when the frictional energy loss that may occur during the response process is not considered, the plastic energy loss is Represented as:

[0023] (4)

[0024] (11) Calculate the energy values ​​under the elastoplastic response using formulas (3) and (4), compare and select the energy with the main proportion as the main energy required for subsequent analysis;

[0025] (12) Select a series of inertial loads with different overload acceleration peak values ​​and different overload acceleration pulse widths. Under their impact, calculate the principal energy under elastoplastic response through steps (2) to (11), and count the cumulative energy value.

[0026] (13) Using the energy accumulation value obtained in step (12), draw an energy accumulation contour map. The number of contour lines is pre-selected as a fixed value and then corrected.

[0027] (14) Extract the contour data from the energy accumulation contour map in step (13), perform numerical fitting on it, and calculate the goodness of fit of the fitting function according to the following formula. Therefore, a suitable fitting function can be selected;

[0028] (5)

[0029] In the formula, and These are the residual sum of squares and the total sum of squares, respectively. , and These are the discrete cumulative energy value, the discrete cumulative energy mean, and the fitted cumulative energy value, respectively.

[0030] (15) Based on the fitting function selected in step (14), adjust the appropriate number of contour lines, and perform numerical fitting on all contour lines in sequence, and count the parameter values ​​of the fitting function each time.

[0031] (16) Determine the final form of the fitting function based on the mean of the parameters in step (15), and determine the error range of the fitting function by calculating the deviation of the key parameters from the mean.

[0032] (17) Based on the fitting function determined in step (16), establish the equivalent relationship between the two sets of overload accelerations with low peak long pulse width and high peak short pulse width.

[0033] Compared with existing technologies, this invention has the following advantages: The energy accumulation-based impact equivalent testing method provided by this invention simulates dynamic impact environments under two different inertial loads. Addressing the problem of acceleration pulse width mismatch and difficulty in achieving equivalent evaluation between existing impact testing methods, this invention starts from the structural impact dynamics of inertial devices during high overload impacts. Through elastoplastic theory and effective differential techniques, it establishes a quantitative equivalent relationship between the peak overload acceleration and pulse width based on energy accumulation. This relationship can guide the selection of inertial load parameters when conducting impact environment simulation tests, thereby effectively reducing the excessively high cost and time required for real-time testing during simulation. This invention can establish a universally applicable long and short pulse width impact equivalent method, providing technical support for the equivalence of different impact overloads and promoting the engineering process of equivalent methods for extreme overload simulation environment tests. Attached Figure Description

[0034] Figure 1 This is an overall flowchart of the method of the present invention.

[0035] Figure 2 This is the physical analysis model in the embodiments of the present invention.

[0036] Figure 3 This is a time history graph of each energy value under elastoplastic response.

[0037] Figure 4 This is a contour map of accumulated elastic deformation energy in the embodiment.

[0038] Figure 5 The figure shows the parameter variation trend of the contour fitting function for elastic deformation energy in the embodiment. Detailed Implementation

[0039] The present invention will be further described below with reference to specific embodiments.

[0040] An impact equivalent test method based on energy accumulation, the overall process is as follows: Figure 1 As shown, it includes the following steps:

[0041] (1) Establish a theoretical analysis model for inertial impact, such as Figure 2As shown, the model is a simplified physical model of the sensor's sensitive structure. In this embodiment, the model simplifies the crossbeam sensitive structure of the accelerometer to a cantilever beam.

[0042] (2) Based on the measured acceleration data from the overload impact test, determine the external inertial load of the simplified physical model in step (1). It is in half-sine form, as shown in the following formula:

[0043] (1)

[0044] In the formula, m is the mass of the physical model, a is the peak value of the inertial acceleration, and T is the pulse width of the inertial acceleration (half a period of the sine function).

[0045] (3) Inertial load determined in step (2) Next, force analysis is performed on the micro-segment units contained in the physical model;

[0046] (4) Based on the force analysis in step (3), establish the governing equations and geometric equations of the physical model;

[0047] (5) Based on the actual inertial device, the material parameters of the physical model are selected. In this embodiment, based on the actual use of the accelerometer, the physical model is made of Si material. Thus, the material parameters such as the density, Young's modulus, and elastic limit strength of Si can be determined, and the constitutive relationship of the ideal elastoplastic material can be determined, as shown in the following formula:

[0048] (2)

[0049] In the formula, E is the Young's modulus of the material. The instantaneous stress of the material during loading. The instantaneous strain of the material during loading. The elastic limit strength of the material. The strain corresponding to the elastic limit strength of the material;

[0050] (6) Based on the constitutive relation of step (5), calculate the mechanical parameters of the physical model, as shown in the following equation:

[0051] (3)

[0052] In the formula, M is the instantaneous bending moment of the structure, N is the instantaneous axial force of the structure, z is the distance from any point on the structure to the neutral axis of the interface, and A represents the cross-sectional area of ​​the structure.

[0053] (7) Determine the initial and boundary conditions of the elastoplastic response process based on the physical model;

[0054] (4)

[0055] In the formula, L is the length of the cantilever beam, x is the distance between any point on the cantilever beam and the fixed end, t is the loading time, and w and u are the deflections in the x and y directions, respectively. , Let be the derivative of the deflection with respect to the displacement at any point on the cantilever beam. , Let be the instantaneous velocity at any point on the cantilever beam;

[0056] (8) Using the finite difference technique, the governing equations, geometric equations, constitutive relations and mechanical parameters in steps (4) to (6) are discretized into finite difference forms. Under the initial conditions and boundary conditions in step (7), the structure is calculated under inertial loads. The time history response process of all nodes;

[0057] (9) Based on the dynamic response results obtained in step (8), calculate the work done by the external forces on the structure using the following formula. ,kinetic energy and elastic deformation energy :

[0058] (5)

[0059] In the formula, For the j-th discrete time, The time step of the discrete difference is... Let be the deflection at the nth node at time j. , Let represent the instantaneous velocities of the i-th node at time j in the x and y directions, respectively. , Let these represent the instantaneous bending moment and axial force at the i-th node at time j, respectively. Let the inertial force at time j be denoted as . , Let these represent the mass and length of the i-th micro-segment unit, respectively. Represents the second moment of the structure;

[0060] (10) According to the law of conservation of energy, when the frictional energy loss that may occur during the response process is not considered, the plastic energy loss is Represented as:

[0061] (6)

[0062] (11) Calculate the energy values ​​under the elastoplastic response using formulas (5) and (6), such as Figure 3 As shown, the energy with the main proportion is compared and selected as the main energy required for subsequent analysis. In this embodiment, the elastic deformation energy can be determined as the main energy.

[0063] (12) Select inertial loads with overload acceleration peak values ​​of 1Wg, 2Wg, ..., 20Wg and overload acceleration pulse widths of 0.1ms, 0.2ms, ..., 1ms. Under these 200 sets of load impacts, calculate the elastic deformation energy under the elastoplastic response through steps (2) to (11), and count the cumulative energy value.

[0064] (13) Using the energy accumulation value obtained in step (12), draw an energy accumulation contour map, such as Figure 4 As shown, the number of contour lines can be pre-selected to a certain value and then modified. In this embodiment, the number of contour lines is pre-selected to be 10.

[0065] (14) Extract the contour data from the energy accumulation contour map in step (13). In this embodiment, a power function is selected and numerically fitted. The goodness of fit of the fitting function is calculated according to the following formula. It can reach 0.99;

[0066] (7)

[0067] In the formula, and These are the residual sum of squares and the total sum of squares, respectively. , and These are the discrete cumulative energy value, the discrete cumulative energy mean, and the fitted cumulative energy value, respectively.

[0068] (15) Based on the fitting function selected in step (14), adjust the appropriate number of contour lines, determine that the maximum number of contour lines is 19, and perform numerical fitting on all contour lines in sequence, and count the parameter values ​​of the fitting function each time, such as Figure 5 As shown, when the number of contour lines is 20, the trend of change has begun to show a large deviation.

[0069] (16) Determine the final form of the fitting function based on the mean of the parameters in step (15), and calculate the deviation of the key parameters from the mean. The key parameters are exponents. The calculation shows that the deviation of the exponents from their mean is less than 4%. Therefore, the error range of this fitting function is 4%.

[0070] (8)

[0071] (17) Based on the fitting function determined in step (16), establish the equivalent relationship between the two sets of overload accelerations with low peak long pulse width and high peak short pulse width, as shown in the following formula:

[0072] (9)

[0073] In the formula, , and , These are the peak values ​​and pulse widths of the two sets of overload accelerations, respectively, and the equivalent calculation is complete.

[0074] The scope of protection claimed by this invention is not limited to the specific embodiments described above. Moreover, for those skilled in the art, this invention can have various modifications and alterations. Any modifications, improvements, and equivalent substitutions made within the concept and principles of this invention should be included within the scope of protection of this invention.

Claims

1. An energy accumulation-based impact equivalent test method, characterized by: Includes the following steps: (1) Establish a theoretical analysis model under inertial impact. The model is a simplified physical model of the sensitive structure of the sensor device, which can meet the dynamic overload response analysis. (2) According to the acceleration measured data of the overload impact test, the external inertia load of the simplified physical model in step (1) is determined ; (3) Under the inertial load determined in step (2), perform force analysis on the micro-segment elements contained in the physical model; (4) Based on the force analysis in step (3), establish the governing equations and geometric equations of the physical model; (5) Based on the actual inertial device, select the material parameters of the physical model and determine the constitutive relation of the ideal elastoplastic material, as shown in the following equation: (1) In the formula, E is the Young's modulus of the material. The instantaneous stress of the material during loading. The instantaneous strain of the material during loading. The elastic limit strength of the material. This represents the strain corresponding to the material's elastic limit strength. (6) Based on the constitutive relation of step (5), calculate the mechanical parameters of the physical model, as shown in the following equation: (2) In the formula, M is the instantaneous bending moment of the structure, N is the instantaneous axial force of the structure, z is the distance from any point on the structure to the neutral axis of the interface, and A represents the cross-sectional area of ​​the structure. (7) Determine the initial and boundary conditions of the elastoplastic response process based on the physical model; (8) Using the finite difference technique, the governing equations, geometric equations, constitutive relations and mechanical parameters in steps (4) to (6) are discretized into finite difference forms. Under the initial conditions and boundary conditions in step (7), the structure is calculated under inertial loads. The time history response process of all nodes; (9) Based on the dynamic response results obtained in step (8), calculate the work done by the external forces on the structure using the following formula. ,kinetic energy and elastic deformation energy : (3) In the formula, For the j-th discrete time, The time step of the discrete difference is... Let be the deflection at the nth node at time j. , Let represent the instantaneous velocities of the i-th node at time j in the x and y directions, respectively. , Let these represent the instantaneous bending moment and axial force at the i-th node at time j, respectively. Let the inertial force at time j be denoted as . , Let these represent the mass and length of the i-th micro-segment unit, respectively. Represents the second moment of the structure; (10) According to the law of conservation of energy, when the frictional energy dissipation possibly generated in the response process is not considered, the plastic energy dissipation is expressed as: (4) (11) Calculate the energy values ​​under the elastoplastic response using formulas (3) and (4), compare and select the energy with the main proportion as the main energy required for subsequent analysis; (12) Select a series of inertial loads with different overload acceleration peak values ​​and different overload acceleration pulse widths. Under their impact, calculate the principal energy under elastoplastic response through steps (2) to (11), and count the cumulative energy value. (13) Using the energy accumulation value obtained in step (12), draw an energy accumulation contour map. The number of contour lines is pre-selected as a fixed value and then corrected. (14) Through the energy accumulation contour map of step (13), extract the contour data and perform numerical fitting, and calculate the fitting degree of the fitting function according to the following formula , and select the appropriate fitting function; (5) In the formula, and These are the residual sum of squares and the total sum of squares, respectively. , and These are the discrete cumulative energy value, the discrete cumulative energy mean, and the fitted cumulative energy value, respectively. (15) Based on the fitting function selected in step (14), adjust the appropriate number of contour lines, and perform numerical fitting on all contour lines in sequence, and count the parameter values ​​of the fitting function each time. (16) Determine the final form of the fitting function based on the mean value of the parameters in step (15). The fitting function is the relationship between the peak value of overload acceleration and the pulse width of overload acceleration. The error range of this fitting function is determined by calculating the deviation of the key parameters from the mean value. (17) Based on the fitting function determined in step (16), establish the equivalent relationship between the overload acceleration peak value and pulse width for two sets of low peak value long pulse width and high peak value short pulse width.

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